CHAPTER 1 ­VARIABLES, EXPRESSIONS AND INTEGERS
1.1 EXPRESSIONS AND VARIABLES
1.2 POWERS AND EXPONENTS
Evaluate and write variable expressions
Obj ­ Use powers to describe repeated multiplication
VOCABULARY ­ MUST KNOW
Factors ­ numbers you multiply together
Product ­ answer when you ___________
Sum ­ answer when you _________ Difference ­ answer when you _________
Quotient ­ ___________
Numerical Expression ­ consists of numbers and operations (no equal sign)
Ex) 4 x 10 4(10) 12 + 6 x 3
Variable ­ letter used to represent one or more variables
What letter not to use as a variable?
Variable Expression ­ consists of numbers, variables and
operations
Ex) 4d 3a + 2 Numbers first, letters second on multiplication.
Do not use "X" as multiplication symbol.
"X" is now a variable.
Evaluate ­ substitute a number for each variable, then
find the answer
Ex) Evaluate 7S when S = 6
7 x 6 = 42 SHOW YOUR WORK!!!!!!!
Ex) Evaluate x + y when x = 23 and y = 17
23 + 17 = 40 SHOW YOUR WORK!!!!!!!!
Verbal Model ­ Writing an expression or equation from words.
Unit Analysis ­ To determine a label for a word problem. 1
Common words that indicate operations. Chart page 6 ­ Learn these!!!
N less than 12 indicates 12 ­ N NOT N ­ 12 Helpful hint ­ Use numbers in place of variables. Isn't 5 less than 12 definitely 12 ­ 5? Whenever you are faced with problems that involve large numbers you can first work the problem with smaller numbers then go
back and rework using the larger numbers
When showing division use a fraction bar verses the division sign.
Trying to use more advanced mathematics ­ WORD PROBLEMS!!!
ALWAYS ask yourself, what do they want to know? Restate the
question, then begin to work the problem.
EX) You plan to provide 2 cookies for each of the f football boys
for a snack. Write a variable expression for the number of
cookies you will need if you know the number of football boys. How many cookies? 2 for each boy ­ If 1 boy ­ 2 cookies
2 boys ­ 4 cookies
3 boys ­ 6 cookies
4 boys ­ 8 cookies
See the pattern? You multiply the number of boys by 2
There are f boys so 2f is our expression.
MAIN CONCEPT ­ Use a variable expression when writing
numerical pattern. Generalize a pattern of numbers.
EX) You spend $.75 a day on a soda. How much have you
spent after d days? $.75 the first day, $.75 the second day, $.75 the third day
$.75d
Show your work. Ex) Evaluate when m = 5 and n = 6
n ­ m
6 ­ 5 = 1 2
1.2 POWERS AND EXPONENTS
8 + 8 + 8 + 8 + 8 + 8 = 8 x 6 repeated addition or multiplication
7
8 x 8 x 8 x 8 x 8 x 8 x 8 = 8
8 is the base
7 is the exponent Power is the result of repeated multiplication
Base is used as a factor 7 times (what the exponent tells you) 13 4 written using an exponent
13 x 13 x 13 x 13 written as repeated multiplication
EX) Write the product using an exponent. (This does not mean to multiply out!)
15 x 15 x 15 x 15 x 15 = t
∙ t ∙ t ∙ t ∙ t ∙ t ∙ t ∙ t ∙ t =
0 to any power is 0!!
EX) Evaluate x
= 3 ( .)
3 3 3 3 = = .7
.7 .7 = 3
Formulas ­ describe a relationship between quantities.
F = 9/5C + 32 How to change C to F
Describe how F and C are related
C = 5/9(F ­ 32) How to change F to C
PERIMETER ­ distance around a figure. (Squares or Rectangles)
Add all sides together (Enclosing a pasture.)
Label perimeter with units (in, ft, cm, m, etc.)
8in
5 in
AREA ­ How much space inside a 3 dimensional space. (Squares and Rectangles) How much carpet to cover floor
2
Label in units
( in 2 , ft 2 , cm 2 , m 2 et.)
To find the area of a square or rectangle multiply the length and width.
AREA = LENGTH x WIDTH
8 cm
6 in
8 cm
15 in
4
Volume ­ How much a 3­D object will hold.
How much water in an aquarium?
Volume = Length x Width x Height 3
Label in units
; in 3 , ft 3 , cm 3 , etc
3 ft
2 ft
7 ft
Ex) Books in my cabinet are stacked that forms a cube that measures 5 feet on each side. Find the volume of the stack of books. 5
WARM UP TO ALGEBRA!!!
A. 96.6 ÷ 2.3 B. 31.5 ∙ 3.4
1.3 ORDER OF OPERATIONS
OBJECTIVE: Use order of operations to
evaluate expressions
NEED ONE AGREED UPON WAY TO WORK ARITHMETIC PROBLEMS
GEMS 1) Evaluate expressions inside grouping symbols
2) Evaluate powers
3) Multiply and Divide from left to right
4) Subtract and Add from left to right
2
EX) 50 / (17 + 3
­ 1)
EX) 3(7.4 x 2.2)
EX) 23 ­ 5 Division Bar ­ 4.2 + 4.8 Compute denominator
Compute numerator
Simplify fraction
EX) 10[ 6 + 8 x 2)
EX) Evaluate the expression when x = 4 and y = 9
a) 10(y ­ x)
b) 3[(x
2
­ y) + 6]
EX) You but a pattern and enough material to make two pillows. The
pattern costs $5. Each pillow requires $3.95 worth of fabric and a
button that costs $.75. Find the total cost. 6